Aresearcher collects a simple random sample of grade-point averages of statistics students, and she calculates the mean of this sample. under what conditions can that sample mean be treated as a value from a population having a normal distribution?

A sample mean can be assumed to be the value from population having a normal distribution when both or either of these conditions is met:

1) The population from which the sample is being taken is Normally distributed. So in this case, if the population of grade-point averages is normally distributed, the sample mean would be treated as a value from a population having a normal distribution

2) The sample size is greater than 30. If we do not have knowledge about the population, but the sample size is greater than 30, the sample mean can be considered as a value from a population having a normal distribution.

step-by-step explanation:

do you have a copy of the table?

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2